970. Powerful Integers #

题目 #

Given two positive integers x and y, an integer is powerful if it is equal to x^i + y^j for some integers i >= 0 and j >= 0.

Return a list of all powerful integers that have value less than or equal to bound.

You may return the answer in any order. In your answer, each value should occur at most once.

Example 1:

Input: x = 2, y = 3, bound = 10
Output: [2,3,4,5,7,9,10]
Explanation: 
2 = 2^0 + 3^0
3 = 2^1 + 3^0
4 = 2^0 + 3^1
5 = 2^1 + 3^1
7 = 2^2 + 3^1
9 = 2^3 + 3^0
10 = 2^0 + 3^2

Example 2:

Input: x = 3, y = 5, bound = 15
Output: [2,4,6,8,10,14]

Note:

• 1 <= x <= 100
• 1 <= y <= 100
• 0 <= bound <= 10^6

题目大意 #

给定两个正整数 x 和 y，如果某一整数等于 x^i + y^j，其中整数 i >= 0 且 j >= 0，那么我们认为该整数是一个强整数。返回值小于或等于 bound 的所有强整数组成的列表。你可以按任何顺序返回答案。在你的回答中，每个值最多出现一次。

解题思路 #

• 简答题，题目要求找出满足 x^i + y^j ≤ bound 条件的所有解。题目要求输出中不能重复，所以用 map 来去重。剩下的就是 n^2 暴力循环枚举所有解。

代码 #

package leetcode

import "math"

func powerfulIntegers(x int, y int, bound int) []int {
	if x == 1 && y == 1 {
		if bound < 2 {
			return []int{}
		}
		return []int{2}
	}
	if x > y {
		x, y = y, x
	}
	visit, result := make(map[int]bool), make([]int, 0)
	for i := 0; ; i++ {
		found := false
		for j := 0; pow(x, i)+pow(y, j) <= bound; j++ {
			v := pow(x, i) + pow(y, j)
			if !visit[v] {
				found = true
				visit[v] = true
				result = append(result, v)
			}
		}
		if !found {
			break
		}
	}
	return result
}

func pow(x, i int) int {
	return int(math.Pow(float64(x), float64(i)))
}